15.1 Excited State Processes

• both optical and dark processes are described in order to develop a kinetic picture of the excited state • the singlet-triplet split and Stoke's shift determine the wavelengths of emission • the fluorescence quantum yield and lifetime depend upon the relative rates of optical and dark processes • excited states can be quenched by other molecules in the solution

15.1 : 1/8 Excited State Processes Involving Light

• absorption occurs over one cycle of light, i.e. 10-14 to 10-15 s • fluorescence is spin allowed and occurs over a time scale of 10-9 to 10-7 s • in fluid solution, fluorescence comes from the lowest energy singlet state S2 •the shortest wavelength in the T2 fluorescence spectrum is the longest S1 wavelength in the absorption spectrum T1 • triplet states lie at lower energy than their corresponding singlet states • phosphorescence is spin forbidden and occurs over a time scale of 10-3 to 1 s • you can estimate where spectral features will be located by assuming that S0 absorption, fluorescence and phosphorescence occur one color apart - thus a yellow solution absorbs in the violet, fluoresces in the blue and phosphoresces in the green

15.1 : 2/8 Excited State Dark Processes

• excess vibrational energy can be internal conversion transferred to the solvent with very few S2 -13 -11 vibrations (10 to 10 s) - this T2 process is called vibrational relaxation S1

• a molecule in v = 0 of S2 can convert T1 iso-energetically to a higher vibrational vibrational relaxation intersystem level of S1 - this is called internal crossing conversion

• a molecule in the v = 0 state of S1 can have the electron spin spontaneously flip, creating a molecule S0

in a higher vibrational level of T1 -this 7 9 -1 is called intersystem crossing kf = 10 to 10 s 3 -1 • observation of phosphorescence kp = 1 to 10 s 11 13 -1 requires that the sample be cooled to kvib = 10 to 10 s 11 13 77 K to minimize the dark path kic = 10 to 10 8 13 -1 kix = 10 to 10 s @ 298 K 10 to 103 s-1 @ 77 K

15.1 : 3/8 Singlet-Triplet Split

• triplet states always lie at lower energy than the corresponding singlet • electrons in singlet states have different spin, thus can have the same position in space - this creates a large electron-electron repulsion energy • electrons in triplet states have the same spin, thus cannot have the same position in space - this reduces the electron-electron repulsion energy • the splitting is inversely proportional to orbital size, because the electrons will on average be further apart • the splitting is proportional to orbital overlap, thus electrons promoted from substituent atomic orbitals to conjugated p-orbitals will have a small splitting

anthracene 12,000 cm-1 tetracene 10,900 pentacene 9,400 ethylene 24,250 formaldehyde 2,996 (oxygen electron promoted)

15.1 : 4/8 Stoke's Shift

10-15 s < 10-9 s ~ 10-9 s < 10-9 s

absorption re-solvation fluorescence re-solvation

• fluorescence and absorption spectra should have a common vibronic band - called the 0-0 band because the transition is from

S0(v = 0) to S1(v = 0) • because the excited state can be solvated differently than the ground state, the 0-0 band for fluorescence is often at lower energy (longer wavelengths) than the 0-0 band for absorption - this is called the Stoke's Shift • a large Stoke's shift allows the excitation wavelength to be far away from the emission wavelength - this is an advantage when measuring small fluorescence signals

15.1 : 5/8 Rate Constants and Quenching

• the rate constant for fluorescence is roughly proportional to the molar absorptivity

ε 5×104 5×103 5×102 9 8 7 kf 10 10 10

• the rate constant for intersystem crossing depends upon the singlet-triplet gap, the smaller the gap the larger the rate constant • the rate constant for intersystem crossing is increased with Br and I substitution into the double bond structure • during the lifetime of the excited state a molecule can lose energy via collisions, this is called quenching k SQ**+⎯⎯q →+ SQ →++ SQheat 1 00

* kq SQ11()↑↓+ii ↑⎯⎯ ()→↑↑+↓ TQ () () common quenchers are oxygen, molecules with heavy atoms, and molecules with unpaired spins

15.1 : 6/8 Fluorescence Quantum Yield

• the quantum yield is defined as the number of emitted photons divided by the number of photons absorbed • the quantum yield varies from 0 to 1 • the quantum yield can be written in terms of excited state rate constants

k f φ f = kkkQfixq++[]

•to obtain a large quantum yield ♦ find a molecule with a large molar absorptivity ♦ substitute a highly symmetric molecule with a group

having a lone pair of electrons (-OH or -NH2) ♦ keep oxygen and free radicals out of the solution ♦ don't use molecules with heavy halogens

ratio naphthalene 1-fluoro 1-chloro 1-bromo 1-iodo

φp/φf 0.093 0.068 5.2 16.4 >1000

15.1 : 7/8 Fluorescence Lifetime

• the decay of an excited state is a first order process, thus it is exponential

0 ⎛⎞t IIff= exp⎜⎟− ⎝⎠τ

• the lifetime, τ, is given by the reciprocal of the sums of the rate constants for all processes starting with the excited singlet state 1 τ = kkkQfixq++[] • the longest lifetime will be measured when no process other than fluorescence is occurring

•when kf is the largest rate constant, the lifetime is roughly related to molar absorptivity

ε 5×104 5×103 5×102 τ 10-9 10-8 10-7

15.1 : 8/8